FIGS. 1-2 respectively show models of a typical Quadrature Amplitude Modulation (QAM) transceiver 10 and a typical Carrierless Amplitude-Phase (CAP) transceiver 12 on a communications channel. Assuming perfect synchronization of the transmitter and receiver, a system may be modelled by the equation v=u*h+n (shown diagrammatically in FIG. 3), wherein v is the complex received signal, u is a transmitted complex symbol sequence, h is a complex channel model, and n is a complex noise signal. The complex noise signal is not assumed to be a white noise signal.
One goal of a characterization of a channel is to find a channel estimate, ĥ, that minimizes the expectation value (EV) of the difference between any given received signal and the expected signal. One formula for EV is shown as Equation 1.
 EV=E{|v−u*ĥ|2}  (Equ. 1)
Once known, channel estimate ĥ can be used by a decoder for determining the appropriate decoder parameters, such as equalizer coefficients.
Further, in a real system, the clocks at the transmitter and receiver are not perfectly synchronized. The difference between the frequency of the transmitter's clock and the receiver's clock is called the baud frequency offset. Typically, the receiver would use some type of a timing recovery loop to track the differences in clock rates. To optimize performance in a packet-based demodulator, it's valuable to also have an estimate of the baud frequency offset to initialize the timing recovery loop before starting demodulation of the packet.
Optimal sequences for obtaining channel estimates have long been understood. See, for example, J. Letaief and R. D. Murch's, “Complex Optimal Sequences with Constant Magnitude for Fast Channel Estimation Initialization”, IEEE Trans. Comm., vol. 46, no3, p. 305-308, March 1998, and Simon Haykin's “Adaptive Filter Theory, 3rd Edition”, Prentice-Hall, Inc. 1996, p 498. However, many methods for channel estimation require high computational complexity or a long preamble, or they don't offer a convenient means of also obtaining an estimate of the baud frequency offset.
Therefore, a need exists for an efficient method and apparatus for determining both the channel estimate and the baud frequency offset estimate. The present invention provides such method and apparatus, wherein a type of preamble sequence and a computational structure obtains both a channel estimate and a baud frequency offset estimate using a minimal number of preamble symbols and having a very low computational complexity.